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Abstract

Introduction

The meniscus has an important role in force transmission across the knee, but a detailed
three-dimensional (3D) morphometric shape analysis of the lateral meniscus to elucidate
subject-specific function has not been conducted. The aim of this study was to perform
3D morphometric analyses of the lateral meniscus in order to correlate shape variables
with anthropometric parameters, thereby gaining a better understanding of the relationship
between lateral meniscus shape and its load-bearing function.

Results

The first principal morphological variation (PMV) was found to correlate with height
(r = 0.569), weight (r = 0.647), BMI (r = 0.376), and femoral condyle width (r = 0.622).
The third PMV was found to correlate with height (r = 0.406), weight (r = 0.312),
and femoral condyle width (r = 0.331). The percentage of the tibial plateau covered
by the lateral meniscus decreases as anthropometric parameters relating to size of
the subject increase. Furthermore, when the size of the subject increases, the posterior
and anterior horns become proportionally longer and wider.

Conclusion

The correlations discovered suggest that variations in meniscal shape can be at least
partially explained by the levels of loads transmitted across the knee on a regular
basis. Additionally, as the size of the subject increases and body weight rises, the
coverage percentage of the meniscus is reduced, suggesting that there would be an
increase in the load-bearing by the cartilage. However, this reduced coverage percentage
is compensated by the proportionally wider and longer meniscal horn.

Introduction

The menisci are crescent-shaped intra-articular fibrocartilages located between femur
and tibia. Meniscectomy persists as a treatment for meniscal tears, despite early
work showing detrimental radiological changes post meniscectomy [1]. This has since been confirmed by many long-term follow-up studies [2-5]. Cadaveric work has shown significant increases in contact stress due to partial
or total meniscectomies [6-8], suggesting that the meniscus has an important role in force transmission across
the knee. Furthermore, the medial and lateral menisci appear to perform differently
in both load bearing and load distribution. Although the medial compartment sustains
more weight-bearing stress [7-9], the lateral meniscus (LM) covers a greater percentage of the area of its compartment
than the medial meniscus [7]. There is also potentially more movement on the lateral tibia [10]. Therefore, the LM may potentially contribute more to load bearing in the lateral
compartment than the medial meniscus does in the medial compartment [7,11]. Evidence of worse radiographic results and higher incidence of late osteoarthritis
(OA) associated with lateral meniscectomy compared to medial meniscectomy may support
this hypothesis [4,12-15], although the convexity of the tibial plateau might also be a factor.

The load-bearing ability of biological tissues is a function of geometry, movement,
and deformation properties; the meniscus is a crucial load-bearing structure that
minimises contact stress by the creation of hoop stresses, thus optimising contact
area [7,8]. Therefore, the shape of the meniscus is especially important in loading. Recent
three-dimensional stress analysis studies have shown the significance of insertional
ligament geometry and meniscus material properties on their load-bearing capability
[16]. However, a three-dimensional morphometric shape analysis of the LM in order to elucidate
subject-specific function has not been conducted. The aim of this study was to perform
three-dimensional morphometric analyses of the LM to discover correlations with anthropometric
parameters and gain a better understanding of the relationship between LM shape and
its potential load-bearing capability. The chosen anthropometric parameters included
height, weight, body mass index (BMI), femoral condyle width and axial rotation of
the knee.

Height, weight and BMI reflect the level of loading applied to the knee, and have
previously been found to correlate with meniscus size and position [17-19] and OA; being overweight increases the risk of OA [20,21] and greater height has been reported as a risk factor for knee injuries [22]. Condylar width is a measure of knee size, and knee rotational position is a geometric
variable that is not known to relate to contact stress; however, as the menisci are
known to move with knee rotation, it was hypothesised that there is a correlation
between rotational position and meniscus shape. BMI is correlated with knee overuse
injury [23], acute knee injury and associated pathologies [24], and degenerative joint disease [23,25,26]; therefore, a correlation with BMI was also expected.

Methods

Study sample

Fifty subjects from the Osteoarthritis Initiative (OAI) were randomly selected from
the “non-exposed” reference cohort (age 56 ± 8 years; height 169.1 ± 9.7 cm; weight
70.93 ± 11.98 kg; BMI 24.7 ± 3.0 kg/m2; 25 male and 25 female). The non-exposed cohort contains subjects for which there
are no symptoms of OA present, no radiographic signs of knee OA, and no risk factors
for developing knee OA. These inclusion criteria enable observation of normal meniscus
function in subjects who are unlikely to develop OA. The data are available at [27].

This study used magnetic resonance (MR) images from the OAI database from groups 0.C.2
and 0.E.1 at baseline. The fat-suppressed, sagittal three-dimensional double-echo
in steady state (DESS) sequence with water excitation (WE) (referred to here as Sag
3D DESS) was selected because it has both high in-plane resolution (0.365 × 0.365 mm)
and a small slice-thickness (0.7 mm). Further information about the imaging protocol
can be found in Peterfy et al.[28].

The axial rotation of the tibia with respect to the femur was quantified by determining
the surgical epicondylar axis on the femur and the posterior condylar axis on the
tibia, measured at 8 mm distal to the joint surface [29]. The anthropometric parameters of weight, height, BMI, and femoral condyle width
were downloaded from the OAI dataset labelled PhysExam00 and kXR_QJSW_Duryea00 from release version 0.2.2; the variables are named P01WEIGHT, P01HEIGHT, P01BMI
and V00CFWDTH. Ethical approval and informed consent were not required as the data
used in this study was from a publically available dataset.

Morphometric analysis of the lateral meniscus

The MR images were manually segmented from sagittal, coronal and transverse views
using Mimics (Materialise NV, Leuven, Belgium) as can be seen in Figure 1. The segmentations were then smoothed using the reduce-noise option in Geomagic Studio (Geomagic, Inc., Morrisville, NC, USA) to achieve three-dimensional
surface models. To minimise the interventions to the surface detail, a single iteration
of noise reduction was used. The smoothness results indicated that throughout the
50 sets of surface models the average distance that all points were moved was between
0.008 and 0.016 mm.

Statistical shape modelling (SSM) as described by Zhang et al.[30] was used to perform the three-dimensional morphometric analysis and reveal the significant
shape parameters. This is a model-based image analysis technique that aims to establish
any linear patterns of variation in the shape and any spatial relationships between
the structures in a given class of images.

The shape of a subject’s LM can be defined by a vector of point coordinates as follows:

where there are n surface points in the surface model. To compute the SSM, an LM surface
model in the dataset was randomly chosen as the reference segmentation. All other
three-dimensional surface models of the LMs were aligned to the coordinate system
defined by the reference segmentation using the iterative closest-point algorithm
[31]. Point-to-point correspondences were then established for each subject to the reference
subject using the multi-resolution free-form deformation algorithm proposed by Rueckert
et al.[32]. A mean model was computed for each set of corresponding points from each LM surface
model (x), and principal component analysis (PCA) was performed to extract principal morphological
variations (PMVs) of linear combinations of point coordinates.

Statistical analysis

The correlations between anthropometric parameters: height, weight, BMI, femoral condyle
width and axial rotation were tested to understand the study sample. The correlations
between anthropometric parameters as the response variables and the PMVs on each principal
axis as independent variables were tested to identify the relationships between shape
and the anthropometric parameters. They were both tested using the two-tailed Pearson
test at a 95% confidence level.

Quantitative measurement of the extracted PMVs

The PMVs extracted from the LM segmentations were used for analysis. Seven quantitative
parameters including posterior horn width (PH_Wid), anterior horn width (AH_Wid),
posterior horn length (PH_ Len), anterior horn length (AH_ Len), posterior horn to
anterior horn distance (PA_Dis), lateral peripheral horn thickness (LPH_Thic) and
lateral peripheral horn width (LPH_Wid), were constructed and measured for each PMV
to characterise the width and length changes of horns (Figure 2). The reference features to standardise the parameters and the position of the meniscus
are shown in Additional file 1. The inferior surface, which is the area covered by the meniscus on the tibial plateau
(Cov_Area, Figure 3) and the area of the gap between the interior surfaces of the anterior and posterior
horns, which is the area exposed to cartilage (Gap_Area, Figure 3) were measured. The coverage percentage (Cov_Pct) by the LM was calculated as:

Figure 2.Seven morphological parameters quantified. Posterior horn width (PH_Wid): the distance measured between the most posterior and
anterior aspects of the posterior horn; anterior horn width (AH_Wid): the distance
measured between the most posterior and anterior aspects of the anterior horn; posterior
horn length (PH_ Len): the distance measured between the most lateral aspect of the
lateral horn and the most medial aspect of the posterior horn; anterior horn length
(AH_ Len): the distance measured between the most lateral aspect of the lateral horn
and the most medial aspect of the anterior horn; posterior horn to anterior horn distance
(PA_Dis): the distance measured between the coronal planes through the middle of the
medial aspect of the anterior and posterior horns; lateral peripheral horn thickness
(LPH_Thic): the distance measured between the most lateral aspects on the superior
and inferior surfaces of the lateral horn; lateral peripheral horn width (LPH_Wid):
the distance measured between the most lateral and medial aspects of the lateral horn.

Additional file 1.Reference points and planes that were used as reference features to quantify the extracted
morphological variations.

Figure 3.The area covered by the meniscus (Cov_Area) and the gap area between the horns (Gap_Area).

The superior surface of the LM, which is the contact area with the femur (Con_Area)
was also measured, and the total contact area of the knee joint (Tcon_Area) was calculated
as:

To understand the relationship between the openness of the horns and the horn lengths,
the ratio of horn distance to the horn lengths (RDL) was calculated as:

For each PMV, the score on the corresponding principal axis in the SSM was varied
from to , (where is the standard deviation along each principal axis) with the scores on all other
principal axes fixed at 0 to monitor the effect of each PMV upon the mean model in
the SSM. The change rates of the quantitative parameters were calculated as:

In which fmean is the quantitative parameter value of the model with a score of 0; fnMode + and fnMode − are the parameter values of the model with a score of and respectively.

Results

Weight is correlated with height, and BMI is correlated with weight. Height and weight
are correlated with femoral condyle width. These results are as expected (Table 1).

The first six PMVs contribute more than 90% of the total variation in meniscal shape
for the sample of OAI control subjects. As a result the first six linearly independent
PMVs were studied. The change rates of the quantitative parameters and significant
features of the first six PMVs are listed in Table 2. Visualisation of the first six PMVs with score of to are shown in Figure 4.

Correlations with the first and the third PMVs were found with height, weight, femoral
size, and BMI. In general the correlations between the PMVs (size, horn openness)
and the anthropometric parameters still exist in each individual gender, although
they are not as strong as in the mixed gender pool. The correlations between PMV1
(size) and PMV3 (horn openness) and weight are no longer significant in the female
group (Table 3). The axial rotation in the 50 subjects is 7.07° ± 7.12° (mean ± standard deviation).
No correlations were found with axial rotation of the knee. Statistically significant
correlations were not found between the anthropometric parameters and the second,
or fourth to sixth PMVs.

Discussion

Morphological data on the LM were captured In this study, and were analysed using
statistical shape-modelling techniques. The correlation between the first PMV (corresponding
predominantly to the size of the meniscus) and the anthropometric parameters of height,
weight and condylar width of the knee indicates that when the size of the subject
increases, the total contact area increases and the area of the tibia covered by the
LM increases as a result of wider and longer horns. However, the gap area between
the horns also increases, which causes the coverage percentage of the LM on the tibial
plateau to decrease. The correlation between the third PMV (corresponding predominantly
to horn openness) and these anthropometric parameters also reveals that when the size
of the subject increases, the meniscus becomes more open. Combining the information
extracted from the 1st and 3rd PMVs suggests that when the size of the subject increases
and more bodyweight has to be transmitted across the knee during regular daily activities,
although the actual area covered by the LM on the tibial plateau and the contact area
of the LM with the femur increase, the gap area between the horns also increases.
This is accentuated by the opening of the horns. In larger subjects, when the knee
is required to bear greater loads, the larger total contact area allows the knee joint
to maintain low-contact stresses, but the percentage of the area covered by the LM
is actually reduced, which implies that the capability of mitigating articular surface
contact-stresses could be weakened and greater stresses may develop in the cartilage.
This might explain why higher risks of meniscal injuries, knee injuries and OA have
been found to be correlated with increased bodyweight [23-26] and height [22].

The correlations between the PMVs and the anthropometric parameters reveal that when
the size of the subject increases, the horns of the LM become proportionally longer
and wider (Figure 5). The elongation of the horns can be seen in Table 2 for the first PMV (size of the meniscus), where the ratio between the distance of
the horns and the lengths of the horns (∆RDL) is decreased when the distance between
the horns (∆PA_Dis) is increased. The increased width of the horns can be seen in
Table 2 for the third PMV (∆PH_Wid and ∆AH_Wid). Therefore, the reduced coverage of the tibial
plateau is compensated by the variance of the shape. This finding suggests that although
larger people generally could have more forces distributed by the articular cartilage
in the knee, the shape of the LM appears to compensate for this by having proportionally
longer and wider horns. One could hypothesise that wider horns are better able to
transmit the circumferential stresses [33] due to higher loading. Secondly, the longer horns would enable the meniscus to translate
more due to knee joint rotation and thus be more optimised in terms of location on
the tibial plateau. This further supports the hypothesis drawn from previous long-term
follow-up studies of total or partial meniscectomy cases and in vitro contact area and pressure studies [7,8] that the meniscus has an important role in force transmission across the knee.

Figure 5.Superior views of the sketches of the lateral meniscus. When the size of the subject increases and the tibial plateau becomes larger in size,
the mean model (black lines) changes size uniformly (black dotted lines) and according
to the first and third principal morphological variations of the statistical shape
model (red lines).

Meniscal size, which is a key factor in meniscus transplantation, has been predicted
from standard variables including height, weight and gender, according to the literature
[17-19]. The results from our study suggest that when using these parameters to predict meniscal
size, the variance of the shape accompanied by the change in meniscal size should
also be considered to achieve a better distribution of the contact stress in the knee.

The overarching intention of this work is to understand the variations in shape and
load-bearing capability of the menisci in both control and OA subjects. To provide
a benchmark with which to compare the OA subjects, we analysed the LM from control
subjects in this part of the work. During regular daily activities, the knee joints
often have to transmit high or repetitive loads. For example, during walking, forces
of up to 300% bodyweight can be transmitted across the knee joints [34], and the forces can become four to eight times higher during running [35]. The menisci are thought to bear 40% to 70% of the load across the knee [6]. Our hypothesis is that the meniscus plays an important role in force transmission;
therefore, in control subjects the shape of the meniscus could be influenced by the
loading, but also should be adapted to cope with the force transmission required during
daily activities. The adaptation of knee menisci to prolonged running exercise has
been studied in rats by Vailas et al. [36]. Significant increases in concentrations of calcium, collagen and proteoglycan were
observed in the menisci after the animals were trained extensively for 12 weeks. The
thickness of the posterior lateral meniscal horns were also found to be increased.
The morphological and biochemical changes seen in the rats were thought to be response
and adaptation for the ability of the meniscus to withstand the excessive mechanical
stress from prolonged exercise. The relationship between shape and load-bearing capability,
however, might be changed in subjects with OA or other joint pathologies, as the tissue
properties and loading conditions may have altered the normal functioning of the structures
of the joint. Future work will focus on analysing subjects with OA to investigate
shape differences between these and control subjects. Further extensions to this study
would include the tibial plateau in the shape analysis, as this is likely to be related
to the meniscal extrusion, which was believed to a possible effect of the complex
interactions among joint tissues and mechanical stresses involved in the OA process
in the knee [37].

Conclusion

Three-dimensional statistical shape modelling was used to extract morphological variations
from surface models of the lateral menisci of 50 control subjects obtained from a
publically available dataset. The morphological variations and anthropometric parameter
analyses show that when the size of the subject increases and more bodyweight is required
to be regularly transmitted across the knee, the coverage percentage of the meniscus
is reduced, which suggests that there would be an increase in the load the cartilage
is required to transmit. However, this reduced coverage percentage is at least partially
compensated by the proportionally longer and wider meniscal horns.

Acknowledgements

The OAI is a public-private partnership comprised of five contracts (N01-AR-2-2258;
N01-AR-2-2259; N01-AR-2-2260; N01-AR-2-2261; N01-AR-2-2262) funded by the National
Institutes of Health, a branch of the Department of Health and Human Services, and
conducted by the OAI Study Investigators. Private funding partners include Merck Research
Laboratories; Novartis Pharmaceuticals Corporation, GlaxoSmithKline; and Pfizer, Inc.
Private-sector funding for the OAI is managed by the Foundation for the National Institutes
of Health. This manuscript was prepared using an OAI public use dataset and does not
necessarily reflect the opinions or views of the OAI investigators, the NIH, or the
private funding partners. This work was done as part of the Medical Engineering Solutions
in Osteoarthritis Centre of Excellence, which is funded by the Wellcome Trust and
the Engineering and Physical Sciences Research Council (EPSRC). The funder had no
role in study design, data collection and analysis, decision to publish, or preparation
of the manuscript.